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# (1) Show that the following space of infinite sequences c

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(1)

0

1

2

i

i→∞

i

i­1

i

2

1

x

2

2x

1

2

n



1

2

n



s

2

s

−1¬x¬1

0

1

1

C([−1,1])

n

0

n

2

n

X

i=1

i

i

1

(2)

2

1

n

i

i

n

n+1

n+1

L

n∈E

n

Lˆn∈ ˆE

n

3

i

−1¬x0

<x1<x2¬1

2

n

2

n00

n0

2

n

2n

n

2

n

m

nm

3

n

−8

0

0

0

2

m

k

pk

1

2

n

n

1

2

n

n

2

n

Y

k=1

k

k

!2



k

k

n k,l=1

!

Q

k>l

k

l

k

l

Q

k,l

k

l

1

2

n→∞

n

Y

k=1

k

k

!2

X

k=2

k

(3)

3

k

pk

1

2

2

Pk=2

k

2

k

pk

1

2

1

P

k=2

k

p1

p2

pn

n

## dense in C([0, 1])?

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